NUCLEAR RELAXATION STUDY OF MOLECULAR MOTION IN LIQUID AND SOLID AMMONIA ACKNOMI.EDOJESIS Co write: Difficult hocai of e dissertation, this is Che most difficult committee. Dr. t. A. Scott, for suggesting this study and providing a numerous very helpful suggestions throughout the course of this work. interesting and informative conversations, and to Mr. Basil McDowell Among the people who had no influence on what is written in this Setzer Cardan, for encouragement through many trying periods, and for careful proof-reading of the manuscript. Finally, I wish to thank Mrs. M. Beth Sercombe for her diligent proof-reading and highly competent typing of the final manuscript. s LIST OF TABLES (a.) temporal development of M *(c) following a 90" pulse ' pc ra cur el LN <R(t^ 8 va. time/T' Theocccical proton T® reorientation correlation . Logj^jCTp vs. lO-Vitenperatnre) . 35. typical parallel tuned sample coil circuit CHAPTER I INTRODUCTION Nuclear Resonance techniques nay be gorles: Transient and continuous wove NMR. Within the framework of form of a lineshape, or frequency distribution, function; whereas in is particularly critical in a lineshape e to be discussed in some detail in Chap. 1 models of molecular motion nicely, ore available from the scientific interesting electronics problem. indicated by experiment, and Pauling cd Fig. I. FREE AMMONIA MOLECULE i considered a discorcion of Che 2s orbital forming intermolecular bonds of an ionic nature (2) known as hydrogen bonds. kcal/mole N-H bond energy (4) gives one some perspective to Che magni- The objective of Chi iasons, but primarily be is is not a trivial task for a multitude ol sarily involves an exchange of energy, thereby altoring the normal able compromise with Nature: We compromise the ability to study a single molecule and look instead at the average motion of an effective- a magnetic field it, the nucleus E - -ytan | Sj (2.2) » - t-I, -CI-1), — •. (2.3) end y is a constant of proportionality, called Che gyromagnedc ratio. he molecular motion and the results obtained by using these characteristic of The Hamiltonian O: and the individual te: is examined in some detail. The general Hamil- rstem la written out explicitly in Sllchcer (6). Hamiltonian that we work with will provide a back door through which are now written out. Since ultimately we ere interested in describing given in Eq. (2.2). Rocaclon of Che molecule docs noc affect this t is spatially and temporally constant. 2.3.2. Buclear Dloole-Dlnole Interaction Tern Eq. (2.5) o -‘ > V - ” 1 * •--K^ 4 V5“'V”“*'“ lk —f'S-V*’" ««■»*- . ...» .. H, ... H . ,.i„- E,. (2.7) Tacts fron the external field 9 . Note the Andrew (8). was first considered in Che classic Bloembergen, magnetic Held ae a nuclear site In a rigid lattice. Van Vleck (10) has investigated this problem in detail and derived an expression for calculating the mean square local magnetic field at a given nuclear nuclei in the solid are allowed. The effect of rapid, isotropic mo- lecular motion on terms A and B is to average the angular factor to aero. Theories have been developed field from the rigid lattice value Co molecular motion. To this point we have considered oi moment along an externally applied magnetic fie electric field gradi- excepclon: In diamagnetic materials cl term whereas Che molecular electric fie the sample without breaking ilar field gradient at the K o - fusTTi < 31 ! - ** * * *■*». V A point of interest in this Hamiltonian is that the I £ operator appears os a squared tern leading to degenerate eigenenergies for the m - +1 states. The factor eq in Eq. (2.13) is dependent on the environment of property of the nucleus itself. It is conventional to define Che term (eqQ/h) as the quadrupole coupling constant expressed in Ha. The quadrupole coupling constant for the case of nitrogen in ammonia is -3.16 KHz at 77 K to -3.08 MHz at 193 K (approximately 3 K below Che normal melting point). The quadrupole Hamiltonian is thus approxi- treated easily as a perturbation as can 2.3.4. Magnetic Interactions of Hudel with Molecular Electrons The Zeeman Hamiltonian Introduced in Sec. 2.3.1. is rigorously consider the magnetic Interactions possible in a diamagnetic molecule actions of this nature are separable into two broad categories: externally applied magnetic field, and b) Those externally applied magnetic field, lt 0 , which has the site. The contribution of R + fl . along fi nay be function of the relatlvo orientation of the molecule with H . This effect is usually of the component of 6. + R along fl affects the Zeeman Hamllconian. each molecular species is exploited tc in both quantitative and qualitative analysis of of a few hundred parts per million would obviously totally wash out liquids the dipolar contribution to the nagnetic field at a nuclear Interactions of type b) prove to be quite interesting in the study Maxwell (16) and Gucowsky and McCall (17). The paper by Hahn and Max- well is particularly interesting because transient NMR techniques ere used. It was found experinentally chat this interaction was lodcpend- K ln . hJlj-Ij. (2.16) Experimentally, we are able to consider the various Interactions tally separate experiments because the wide difference in magnitude perlmental apparatus to be sensitive only to small non-overlapping frequency intervals at the ccaccr frequency corresponding to a Zeeman ^ with the nitrogen nucleus and b) information obtainable by ) Indiroct spin-spin interaction molecular proton. Intramolecular dipole-dipole interaction among CHASTER III INTRODUCTION TO NUCLEAR MAGNETIC RESONANCE AND RELAXATION *0 - H ■ 3fcpV«X#l)« (3. The magnitude of Che scacic nuclear magnetic susceptibility, x Is typically lo" 10 to 10' 11 . Therefore, for a laboratory field of trivial experimental problem using static techniques. Static ccchr ques are difficult experimentally and not very fruitful when one la interested in the study of molecular motion, thus other methods mua 3.2. The Nuclear Magnetic Besonance Phenomenon »e have already established that the effect to be measured is qui small and Is likely to require correspondingly sophisticated experi- mental techniques. Highly elegant techniques have been devised to nal which Is amplified in some cases over as any signal which has no correlation wi in electrical slg- snall electrical sig- iefine quite generally nuclear signal. This experimental techniques; so for lar momentum as well as a magnetic moment. The equilibrium nuclear moment but also a total static angular momentum X which Is related These quantities are of id quantum mechanically. Although what follows will appear strictly classical, i given that l! - II £ and at t ■ . The temporal development " we transform Co a coordinate system with a cod ling the relationship on p. 133 of Goldstein (2! a - s - - t B 5 ation except we enclose the sample in a coil of wire, stationary in the lab frame with its axis normal to It , then a voltage is induced in the coil as a sinusoidally varying change in magnetic flux with a funda- ducer, mentioned earlier, from which we obtain the signal voltage. This is of course a nonphysical situation os the Boltzmsnn distribution is ately begins to seek equilibrium. Furthermore, we have assumed that of 8 small, laboratory generated perturbation to the Zeeman Hamiltonian, let the perturbation be the application of a voltage. [3. 9) to the coil surrounding the sample. For geometric simpllficetion we position the coil as shown in Fig. 3, with its axis along the y axis fij - -JlHjSinwt, <3.10 component rotating in a sense opposite Co chat of the free precession of the nuclear spin system has negligible effect on the spin system rotating in such a manner that it lies out the x axis. Our initial conditions are such that at t » 0, H ■ M 1c and both Che lab and ro- (^j* - B*xy[B 0 + “)1!* + Hifl. (3.11) 2yH,' Generalizing, Che pulse duration fc He have implicitly assumed chac is approximately uniform over possess certain lower bounds which depend on Che sample studied. complete. To measure the equilibrium magnetization of Che spin system: He simply allow the spin system Co come to equilibrium immersed in an applied magnetic field, apply a z/2 pulse to the coil thereby rotating down into the x,y plane, then monitor the voltage induced in the le electronics, |H | may be calculated. :. Transient N> wave NMR (CtfNMR) and transient 1EO (TNMR), as Che response ence in the two methods arises primarily from differences i sal equilibrium is noc appreciably affected. The absorption of energy applies rotating ^ fields of such a magnitude that the Boltsmann pop- the following two distinct experimental steps: distribution function centered about H with g(H)dH defined as the /g(H)dH - 1 . (3.18) 8* - eah* + a/. (3.i9) s width of the distribution function g(H). W about Hjd down to the -‘■>’1 axis. This condition is sometimes not large dipole coupling sometimes present, but in liquids it is usually quite easy to satisfy. For this discussion we assume this condition any significance ft Fig. 5(a.)dcpicts Che situation os seen j • 90° pulse. Fig. 5(b) Fig. 5. 'IDEAL' SPIN SYSTEM BEHAVIOR FOLLOWING A 90 - PULSE ble migration co Chennai equilibriun. We noce Chat scadscical chcr- pulse has Che e£fecc of equalising Che spin scace populacions and cre- pulse Che veccor sun of Che nuclear nagnecizacion/unic volume is ft(o) * • The cwo processes leading Co ulcfmaee descruccion of processes is implicitly concained in Che lineshape function, f(u). M y *(T) - » [ scribing loss of crsnsverse nagnetleotion. Note that implicitly this Includes processes governed by T^. Thus the lineshape function DETECTED SAMPLE G(t) ■ / f (v)cos 2svt 2 i lv ■ 2r/f(v)EXP(-2niv)dv. multiply through hy EXP(lui't). EXFClu't) /f (ui)EXP(-iut)du “ ^V, (t)BCP(liu't) (3.31) /duf(u) /EXP[-lt(im')ldt - - /V (t)EXP(iw't)de. (3.32) /EXP(-it(u-ti'}]dt - 2ir6(W), (3.33) J(m')-jJj /V d (t)EXP(lu't)dt . (3.34) Thus wo have demonstrated that the FID and the distribution function previously defined. f(cd) is defined by M n " (3.35) Mote that all odd moments vanish as a result of the even parity of f(u). The importance of determining the moments of a lineshape is twofold : a) Knowledge of the various lineshape moments provides de- tailed shape information; b) Van Vleck's (10) classic calculation re- veals the equality of Che mean square local field at a nuclear site ly calculate the second mo- actioos with neighboring I and S spins. This equation is valid only if all spins are in equivalent lattice positions. 2 3Tjfi 2 I(I+l) ^ (1 - 3cos 2 6 1k ) 2 I species whore r^ fc are the respective intranuclear distances. This calculation is quite tedious for nuclear configurations of little symmetry. Great simplifications in this problem are usually possible however thanks Co the rapid r decay of the squared dipole-dipole interaction. One may ocher simplification occurs for the case of a powdered sample, for which Eq. (3.36) averaged over all angles bccoces, •&¥»«> i •?. ™,SI. -■ l(v * V - JltotCv - xHx, ..-te ir polycrystalline sample i my cases, satisfactorily represented by a Gaussian le normalised Gaussian curve is given by le associated FID by substitution o Eq. (3.43) into i (3.45) motion is very rapid, the Lorentaian lineshape is sometimes a better approximation to the experimental curve, Eq. (3.29) gives the follow- ing relationship for the FID when the Lorenczian lineshape function : defined in Eq. (3. 26) at '(b) illustrates f(u) obtained by the method of CUE empirically fit as well as possible to FREQUENCY (kHz) Fifl- 7(b), SOLID NHj LINESHAPE FUNCTION THREE TEMPERATURES , - .-ti for the coaplete spin systea to lose cessional state for a given nucleus is T_, as previously defined. Each sites , i.e. , we expect different values of w rna for different types of which contribute to the averaging process and further narrow the lino. !r angular factors appearing ability of high energy Zeenar The Lorentaian shape function is hi; k -i?-«hv 4 ' AMMONIA (PROTONS) liquids , lecular self-diffusion through an inhomogeneous magnetic field. »(+)»(+-) - X(-)«(-f), - -2n[N(+)W(+-) - »(-)W(-«). Using Eg. (3.59), we find ^--2W„[N(+) - N(-)e'*V kT ]. Eg. (3.59) has the value, VW» 3,2 , io- 4 and (3.64) we see that the populations of the two thermal equilibrium are very nearly equal. Doing the id that Bq. (3.65) reduces tt approximations, nevertheless provides an excellent working approxima- tion for determining Tj, even in solids. The most fundamental assump- tion used iu the derivation of Bq. (3.69) is that which permitted the use of statistical techniques, l.e. that between any two spins there interaction, and on the average is temporally indistinguishable from any other possible spin-spin interaction. This assumption is rigor- ously satisfied for the magnetic dipale-dipole interaction between because the motion of these spies is clearly correlated. & great deal decay constants and different weighting factors. Eq. (3.69) is, how- INTERPRETATION OP EXPERIMENTAL RESULTS 4.1. Outline of Experimental Results mention of tile method used. A thorough description o 1 If Linevidth of CWNMR Absorption Curve X. Region of temperatures studied - -1 to 195 K 3. Method of measurement - CWNMR using magnetic Calculation of Second Moment of CWNMR Lineshapes 1. Region of temperatures studied - —1 to 195 K 2. Magnetic field - 1.7 kG - Calculated from CWNMR llneshapes Measurement of vs. Temperature for Zeeman 1. Region of Temperatures studied - 195 Co 239 K 1. Region of Temperatures studied - 195 to 239 X 2. Magnetic field . Measurement of T 2 vs. Temperature for Protons 1. Region of Temperatures studied - 195 to 230 K All work reported herein was performed at an almost constant pres- sure over Che sample of —20 lb/in 2 absolute. The normal melting and boiling points of NH^ (1) are respectively 195.36 and 239.76 X. The anomalously high boiling point for a member of the Group V hydrides is attributed to the strong hydrogen bonding characteristics of the The solid phase crystal structure of Nil. rained using single crystal and powder X-ray be considered to be a slightly distorted fee lattice with each molecule neighbors — all molecules are in equivalent positions. The distance boor, reported In Che literature (31,32). The mccastable ferns occurred when NH 3 was deposited from Che gas phase onto a surface which was kept at approximately 77K. Our experiment was performed in such a manner as to exclude any possibility of forming a metastable phase. A complimentary lattice structure study of polycryatalline M> 3 was made by Seed and Harris (R-H) (33) using neutron diffraction techniques. Neutron diffraction studies give average positions of the nuclei whereas X-ray diffraction reveals maxima in the electron cloud distribution. He expect the neutron diffraction measurements Co be of more use because it is the average internuclear distance chat is associated with NMR N-N distance are within experimental 1.005 * 0.023 8 is much * 0.004 8 (1,34) than ti X-ray powder work has been done on NHg to 4.2X (32) and no crys- l structure change from the high temperature structure is observed, it capacity measurements from 15K Co the vaporization point (35) 'eal a sharp transition only at Che melting point. The heat oa- iity data do display subtle inflections . in the curve at approxi- et of different modes of molecular motion, a presumption supported this work. Thormal conductivity of solid NH 3 in the temperature . but the thermal expansion data of Menzhelll and Tolkect temperature region 24 to 175 K are Interpreted taking ir molecules. (37), a. work. Hydrogen bonding of kilocalories per mole. Torsional vibrational moi to molecular torsional oscillations about axes n< A quite interesting and important experiment performed by Lehrer as a function of temperature from 77 K to the malting point and the NH 3 and SDj. It is pointed out that torsional vl molecular symmetry axis, which is also the axis of the field gradient tensor, are not effective in reducing the quadrupole coupling constant; theory in conjunction with Reding and Hornig's (38) va] between molecular reorientation and torsio amplitude libratlons of a molecule within well are referred tf frequency given an excellent f] interpret these results to mean that lit I clarify the distinction s crystalline potential is torsional oscillations. Molecular reorienta- ■°n will refer to a physical rotation of the molecule, e.g. a rota- ■on of the NHg molecule about its C 3 axis through 2*/3 radians — from is position of stable equilibrium to another. The structure of liquid has been determined by X-ray diffrac- on work performed by Kruh and Pets (39). The liquid was studied .1 temperatures. They interpret tt radial distribution function at 199 K to indlcste t[ an ammonia molecule has eleven neighbors, seven at £ 3.56 X and four at 4.1 X. The liquid structure beat the interesting speculation of a highly ordered liquid state when confronted with these results, a speculation not supported by nuclear relaxation results. Seoricntation in the liquid state is indeed quite The application of detailed theory to the experimental immonia io order to aeparate Che varioua contributions cusston applies both to the solid and Che liquid state. The physical difference between the molecular liquid and solid scaces is character- ised by the inodes of molecular motion which are thermally activated. account of the problem chan chat given here may be found in lectures by Powles (40) and Bloom (41,42). The problem at hand is quite formidable: To separate the various contributions to tha spin lattice relaxation time, T^ P , and interpret what mode of molecular motion leads to a specific contribution. The separation is conveniently effected through the assumption that Eq. (3.69) may be written in the form: „ , , / M - M(t-O) , Proof of the validity of this assumption is not j retically, but empirical confirmation leads to v( Che assumption is widely used. It is obviously t A. ) l/xj ntra d - the intramolecular dipole-dipole term: This tern ecule. It seems quite generally valid to assume that the molecular bonds are rigid; therefore, magnetic fluctuations which stimulate Zee- man transitions are caused strictly by fluctuations in the angle 8 to intermolecular dipole-dipole interactions, but in liquids both terms are typically of the same order of magnitude. B. ) l/l!°" C d - che intermolecular dipole-dipole interaction term: The magnetic field fluctuations in this case are produced by dipole-dipole interactions <Eq. «.6» between spins on different mole- cules. If molecular self-diffusion and reorientation are completely independent, the effect of this term is governed only by che frequency and magnitude of molecular collisions. This term will Chen contribute information concerning molecular self-diffusion. C. ) 1/T^ - The spin rotacion interaction term: The spin rotation che magnetic field produced by a rotating molecule. Fluctuations in this magnetic field caused by collision modulated molecular rotational states, i.e., changes in che molecular J quantum nueber, stimulate nuclear Zeeman transitions if the fluctuations ore rich in the tarmor frequency Fourier component. Ibis term is usually important only around the critical point of che liquid. For the case of ammonia 1/T^ r has been measured by Smith and Powles (43) and found to be of little importance in the normal liquid region. Thus we are justified in not considering the spin-rotation interaction in this work. D. ) 1/Ti - The electric quadrupole interaction term: If a nuclear occur about Che symmetry axis of the molecule. This presumption is well supported by the l \ <iuadrupole resonance work of lehrer and 0 Konski (14). We thus consider the following model: The proton nuclear relaxation is governed exclusively by inter- and intramolecular dipole-dipole interactions modulated by the molecule undergoing hin- dered rotations about the symmetry axis to the three possible posi- tions of stable equilibrium. 1 be a stationary random process don time t c , which is roughly :h may be characterized by a correla- r c obeys an equation ol e form (see Abragara p. : che barrier hlnder- stant, and E fl is Che activation energy calories/molo. Eq. (4.4) is called the As a first approximation to Eq. (4.3) we assume all terms on the right hand side are negligible but the first. Hilt and Hubbard (H-H) (44), using density matrix formalism, have developed che theory for nuclear magnetic relaxation of equilateral triangular configurations symmetry axis. They consider both the cases of a molecule undergoing random jumps between three equilibrium positions and a molecule under- le definition ol ’.- 4 . experimental work on polycrystslline samples. Fig. 14 depicts a comparison of this theory vi theoretical multiplied by values better if the sum of exponentials in Eg. a single exponential to take into account, in an ad hoc manner th« effects of ineermolecular dipole-dipole interactions. One must hot ever assume a quite largo intermolecular proton-proton interaction it observed non- Fig. M. LN IM, RECOVERY) vs. TIME - PROTONS 2 / EXP(-t/T°)sinSd3. Thla problem required the use of Simpson's numerical integration pro- cedure to evaluate the equivalent Integral, 4CtJ> 8 - / EXP[-t/lJjd*, (4.22) where the substitution, x - cosS. uaa nnde -n,- , , X Msa, was mace. The integral waa approxi- mated by 10 Intervals, i.e., x - 0, 0.2, 0.3 ... l o and the cal lation was performed using a Hewlett-Packard 9100A computer. This integration procedure waa carried out for at least three different values of e for each value of w^. For a given value of « o t , the corresponding l‘ was available from the slope of ■ in / EXP[-t/lJ]dx (4.12) vs. t. One may not rigorously define a single T? for the M (t) re- covery expressed by Eq. (4.11). He find however that Eq. (4.12) is a quite linear function of t (see Fig. 13) and . single ij governing the !. Log T c . The four frequencies used in the experiment and chat the curves corresponding to different ^ are indistinguishable in the short correlation time limit ((w t ) 2 « l). He now proceed to obtain an expression for vs. Tj. prom Tj is directly proportional to V but this is not a. rigorously valid expression. Assumption, The actual physical situation is such that, in the long correlation time limit, T 2 ® » kr i/r Fi} 15. LN <R( I )> s *5. TIME -i- T' quite well justified experimentally it shown by the high linearity of the pic L ° T '' UI “ + ioV“ ’ ir regression techniques Co fit t tnts in the linear low temperature region of Figs. Eq. (4.13), one obtains four values of E which s thin statistical error. A weighted overage over t is performed using as weighting factors the inver. a 991 confidence factor with each estimated standi The following value o sxact theory predicts nearly single recovery in che low l 4 of ref. 44), whereas in the short correlation time limit it true. Thus we expect our experimentally determined T^ accurate in the long correlation time limit. Secondly, che s temperature is increased, of thermally a grcssion fit of experimentally obtained values of LnR(t) vs. t (R(t) mally activated molecular ((ms) ’j, )'aoi relaxation paper that a single exponential recovery is a very good approximation to the exact theory when (w 0 t.) 2 * 100. Ho observe from this figure that when (“ o r c ) ■ 100, * 13.2 T', where T? is the effective intramolecular spin-lattice relaxation time and T' is defined by Eg. <4. 7). For « 0 - 2x x 20.8 MBs we calculate the following values r - 1* - 61 horizontal large separation of d (4.17) t, s sixth power of the nuclear separation. He have .button to range from 0.04/1^ i t contribute from 0.85/1®^ to 1-86/1®,,, with a most probable value predictions and our experimental T,** of 1.27/1*^.. Hi results, whereas the ( 0 -T) values do not, not due to experimental uncertainty, but the different physical quantity measured 10 methods is quite possibly rather a manifestation of tioned previously. X-ray diffraction measurements give information concerning density peaks in the electron cloud, not the nuclear posi- tion as does neutron diffraction. Recall chat molecular bonding in NHj is such that Che molecular electron cloud is heavily concentrated about the nitrogen nucleus, leaving the protons relatively bare. In the solid each proton forms a hydrogen bond with a nearest neighbor molecule through mutual electrostatic attraction between Che proton and the lone electron pair of Che neighboring molecules. It Seems quite feasible that the difference synthesis, performed by Olovssen- Templaton, 4.4.2. Interpretation of Proton linewidth Baca We presented In Sec. 3.4.1. a qualitative picture o( the phenon- enon of linewidth reduction in solids through raolecular notion. The T ■ Tj. (4.18) We also showed that T, is roughly equal to the inverse of the linewidth t„ • (6o>) -X - (4.19) transitions quite effectively. which the linewidth should beain to undergo a sharp reduction. The value obtained in this Banner (-59K) agrees quite favorably with the onset of the first linewidth transition as depicted in Fig. 18. We le linewidth transition which is c* id rotation of the molecules at le observes from Fig. 18 two additional points of Interest dis- in eddltional llnewidth transition, beginning it interrupted before completion by the solid-liquid •nd linewidth transition is of particular interest because it marfcs the activation of a motional process com- pletely distinct from symmetry axis hindered rotation. We speculate cules, or molecular aelf-diffusion-note that molecular self-diffusion must involve isotropic reorientation. made; however, one may obtain a very good estimate oi and Eq. (4.19). By direct analogy with lich Eq. (4.19) is valid, i.e., a plot of t c2 , the correlation time ir the second process, vs. absolute temperature will cross the (Su)~‘ irve of Fig. 17 at T = 180 K. This point on the graph corresponds ti io possible to determine s to an accuracy of approximately linewidth The theories are difficult to ui required. Waugh and Fc make suitable approximations to a very simple tl the following approximate relationship relating of a linewidth transition cure of the transition midpoint. This relationship agrees within 10% of more detailed (but not necessarily more accurate) theories. For comparison, Eq. (4.21) gives a value of 2.4 kcal/mole for the activa- Eq. (4.21) we estimate the activation energy The question of why tl provides a nice case for discussion of the relative sensitivity of the Ice this opportunity in answer to the question key to this question. The linewidth measure- orved to be extremely sensitive to molecular 1 where Eq. (4.19) is approximately satisfied ither frequency. The llnewidth is a characteristic of the solid a through CWNMR techniques is fixed b] Eq. (4.23) is to TNMR what Eq. externally ■ nay study by TNMR is a laboratory only by how cleverly we design our electronic appa- usually accessible. A book describing these techniques in Me used the results of a second n ing the T^ data; the calculation is (33) lattice and molecular parameters ore used. Since Second neighbor protons (Protons mutually H bonded t( points (circled) were obtained by Gutowsky and Pake Clearly the most startling contrast with which la predicted rigid lattice value of Che second me Jhich is longer even than Che spontaneous transition •d Indicate. Clearly the Tj measurements predict no t, illustrated t as profound, is the large barrier. Considerable effort ha* many times in the literature, is triangular configuration of spin is rotating at an angular rate greater thai The resolution of this problem requires molecule through its hindering potential Fort has been expended at the University of i classical rotation of a e calculated rigid dent) the classical expression of Andrew and Bersohn should Assuming than all lattice distances esFsnd according into fij - M°/(l + 04T) 6 . This re] of validity, edT is so snail that terns of order higher than first are negligible. Thus, one has M 2 - M°/ (1 + fadt). We used the ex- tion of a fundamental difference in the quantum mechanical tunneling where it is predominantly classical) would offer some valuable infor- s peculate that the llnewidth transition occurs because the motion in- volved changes from a predominantly coherent character, at very low Interpretation of Nuclear Magnetic Relaxation Data in the number of degrees of freedom and relative magnitude of molec- a typical isotropic molecular reotientational time si rapidly to a vacent lattice position, is invalid for describe a strongly bonded polar liquid such as ammoi »**«!<■ ^■f(4*]V t,- i (4f>, ■»«:«>■ il log of Eq. (4.25), one has an Rg.20. LOGJT'I vs. lOV' (TEMPERATURE) pessimistic + 102 uncertainty previously. (64) for Che HD free molecule (200 + 20 conclusion is drawn thee lictle hydrogen bonding is present Lc hydrogen bonding in liquid annonia is completely work strongly supports the X- ly diffraction (2 e qQ/fi only through distortion ol by X-ray arJ heat of vaporisation work. .(t) - Eq . (4.30) because its weighting facte «.32) Richards (68) has proved that My* ■ R(t) for the sane physical approx- that the relatively strong intraaolecular in isotropic reorientation. a. i . «Ai a , ..mg’* .,«(;)• ».» !;L c fora Uf-S We discussed qualitatively 14 N nuclei on two molecules are not in the same state when chemical 1 n J 2 S(S + 1) where S - 1, Che 14 » spin, and Uj, and w s are respeeeivcly Che Larnor out the multiplet structure end narrowed the observed singlet to e experiment Indicates that HjO is a fantastically efficient catalyst combine Eqs. (4.33), (4.35), (4.36), (4.38) and (4.41) Co write the theoretical expressions. We denote by a subscript t that these values (4.42) (4.43) In Sec. 4.5.1. we calculated Che rotational correlation cine vs. alternate approaches. We thus feel that the values calculated for I- using the solid state shifted value of the quadrupole coupling 8 S constant (3.47 MHz) may be used for r^ in Eqs. (4.42) and (4.43) wi ware taken from ref. (70). Pig. 23 depicts a comparison of perimental results with those of Smith and Powles (43) and ref. (43). The actual experimental scatter of our points, taken at nine different temperatures, is represented as heavy vertical bars to minimize the experimental deviations. Mote that the theoretical data display. One might easily explain a slight difference in the absolute value of different experimental results in terms of slight perimental curve is approximately equal to chat of Che other curves has not been satisfactorily explained; possibly a clue could be ob- tained through an isothermal measurement of vs. sample pressure. Tj™. Simplification of Eq. (4.43) may be achieved by noting that FlgSSLOGj T, ) vs. IC{/(TEMPERATURE) suitable for fitting experimental data by linear regression. We use resenting T?P. One obtains from the linear regression fit a value roton chemical exchange activation energy. The error value is considerably lover than one might expect from kcal/oole. It is conceivable that the proton-proton exchange actlva- efflciency with which H^O impurity in destroys the proton c INSTRUMENTATION AND MEASUREMENT PROCEDURE Matheson Co. and found to be 99.9991 pure NH„. A first prerequisite purity. In particular, oxygen contamination was to be avoided. The by heating the system to above 370 K using s heat gun. This process pressure system. The sample system circuit remained intact throughout thee of ref. (43), indicating a slight impurity. The sample was (roughly three days), the proton T^ values increased slightly, reach- ing a limiting value of ~ 5 sec at 198 K. A temperature run was made points throughout the temperature samples again and taking spot Perfectly consistent results were obtained from both samples in the Fig. TEMPERATURE CONTROL CRYOSTAT surrounding the sample chamber and by providing a tic exchange ga with a slowly boiling cryogenic liquid, and then allowing heat ti as follows: 1.) Three $32 varnished copper wire leads for the heat- ers — electrical resistance of each is 0.6 Ohms, 2.) Four 636 varnish- Mueller bridge xwer input to the bomb must equal the energy lost * cryogenic bath, IE one expects an equilibrium f the bridge is out of balance an error voltage is in- Kaithley model 149. The magnitude of the error voltage gain setting of the Kelthley. The polarity of the error voltage is determined by whether the bomb is too hot or too cold relative to the desired temperature. If the bomb is too cool, one increases the power slightly different input power. We provide this slight variation in +10 Vdc) produces roughly an equal change In voltage across the bomb of the out-of-balance signal. This quadratic behavior provides ex- supply. A Heathklt model PS-4 regulated power supply is not a part of the control loop and is used as a booster to facilitate rapid changes sensitivity setting of the Keithley. The temperature stability fig- ures presented earlier are based on a sensitivity of 1 uV full scale with 6 V applied to the Mueller bridge. Mo loop instability was ever power input to the cryogenic bath and because it facilitates setting the average heater bias voltage. Fig. 27 illustrates tho average pressure in the cryostat vacuum jacket was approximately 10" 4 Torr V control, has a steady euw CHAMBER TEMPERATURE BOMB value. Fig. 29 Illustrates the results of the oeasurements plotted ACROSS SAMPLE (K) sumption, Eq. (3.69) may be used to measure T.. this manner after the first pulse, with M 0 ; likewise, if the 90” pulses v 4 C0 - v 4 (o)[i - stn-t/Tj)!. mental data using Bq. (5.1). One plots Ln(l - V 4 (t)/V 4 (0)] vs. t advantage of illustrating immediately: (1.) The precision of the 90° pulse tuning and (2.) any non-linearity in the recovery. If the 90° pulse is tuned correctly the straight line should pass through the origin, if not the intercept will be finite. One should be particu- ■° Relaxation T: al field gradient; the field is largest at the center and decreases The magnetic field distribution funcelon g(\») is written I ting echo maxima for different T , ia modulated by Che factor EXP(-t\), V (t) - V (0)EXF[ {-t/T.) + (5.8) >uld plot ln[» (t)/» (0)1 vs. t All values of M2 calculated were corrects! (5-10) The terms u n and H m in Eq. (5.10) are, respectively, the modulation peek-to-peak by the oscillator. The frequency of the rf should be approximately equal to that of the absorption line center frequency. The gating circuit, actually an Integral part of the pulsed amplifier. the power amplifier PULSE SPECTROMETER ELECTRONICS Oscillator The gated amplifier tor, Inc. Model PG-650-C pulsed oscillator. eral Radio type 805-D standard signal genera capable of pulses of maximum length roughly able droop. Twelve output coils provide a t . Type 805-D standard signal generator wa roughly +50 parts in 10° over 8 24 hour that this additional SI available through the i is unnecessary with the suppression now Hi Fig. 33(a). CONFIGURATION USED FOR 90’- 1 -90" PULSE SEQUENCE Fig. 33(b). TYPICAL DATA OUTPUT FI ly trigger the recording device 6 imply sliding two switches. The meet from this procedure. Fig. 33(b.) illustrates the typicnl provided by s Tek 162. The pulse from each Tek 163 then triggers s Fig. 34(a.) illustrates the configuration used for a Carr-Furcell © . NKNNKKNKK I l_l l_l L.l © U — I — 1 — I — I I 1 I l_ Fig. 341b.) OUTPUT AT POINTS INDICATED IN Fig. 34 (o.) % «W\ a :± i/ |VVVVua/ Fig. 34(e.) TYPICAL OATA OUTPUT FROM CARR- PURCELL SEQUENCE amplifier, b.) the wideband rf amplifier and c.) the detector cir- by the amplitude modulated rf carrier, and the postamplifier primarily The requirements placed on the detector and postampllfler are filtering process whereby, ideally, the detector is perfectly linear biased into a region of high linearity. This is done most effectively liodo rectification. Distortion will, of course, be intro- !. It oust linearly amplify the rf and have a bandwidth. Modifications of the ir amplifier and PA-620- tn additional 20 to 25 db gain, application or an rf pulse, 2.) the time t,, following Che applies- principle, when applied Co this situation, predicts that the uncertainty a - wMNn/tt ) g(") - i L - w) (5.12) .Fig. 35. TYPICAL PARALLEL TUNED SAMPLE COIL CIRCUIT 7. ARENBURG illustrated in Fig. 35, but with the diodes acting like an open switch. of source Impedance optimization cannot be overstressed when one must *“ 30 usee was obtained with this circuit at 3.3 XHz; additional diode PA-620-L preamplifier (sec Fig. 37). The relatively strong proton re- This brief linewidth and second l illustrated in the operational configuration oscillator (99) constructed i FI* 38. BLOCK DIAGRAM OF THE CONTINUOUS WAVE APPARATUS for work with samples having long T^. power amplifier. The Ling model TP-100-2 4 ‘ ikfimS !Ar»v- ■ S,tKVASS.‘-’ Physics Teachers. of the candidate's supervisory corsaittee and has been approved by al College of Arts and Sciences and to the Graduate Council, and was ap proved as partial fulfillment or the requirements for the degree of Dean, Graduate School £■ H. Mad E. H. Hadlock